The Euro periphery's problems would be solved if it cut its costs, i.e. if it became more competitive vis a vis Germany. That could be achieved by a few years of excess inflation in Germany.
It can be argued Germnay is MORALLY obliged to endure years of uber inflation so as to help the periphery. But that wasn’t down in black and white when the Eurozone was first set up. Quite the reverse: it was obvious from the way the system was set up that it was the less competitive countries that would face elevated rates of interest for money they wanted to borrow if they lost competitiveness. I.e. the burden of adjustment was placed on countries that lose competitiveness.
What Germany could do is approach periphery countries and say “We’re happy to change the rules of the game and endure a few years of excess inflation as long as you pay us something for the inconvenience.” That way, everyone (hoffentlich) would then be happy. Germany wouldn’t lose, because the payment they get from the periphery counterbalances the costs of excess inflation in Germany. While periphery GDP rises and hopefully by more than the fee paid to Germany.
Alles would then be in ordnung.